I What was there before everything came to existence?

[Hugh de Launay]

This is not correct. It is possible to have a topology which is finite but is without a boundary

I accept your correction because I have not studied this kind of topology -- unless you mean curved surfaces that can be made to be unlimited in two dimensions. May I trouble you for an explanation or a reference?

 

[Hugh de Launay]

rid yourself of the misunderstandings that there even COULD be an edge to the universe or something outside the universe and the idea that "no edge" implies infinite.

What do you think I meant by "edge" and by "universe" and by "no edge"? How complicated do you want to get?

 

[jbriggs444]

I accept your correction because I have not studied this kind of topology -- unless you mean curved surfaces that can be made to be unlimited in two dimensions. May I trouble you for an explanation or a reference?

Consider as a simple example, a circle. It has one dimension. The points on the circle can be given coordinates from 0 degrees up to but not including 360 degrees. There is no edge. Yet it is finite. The circle wraps around on itself.

You may object that the circle is embedded in a two dimensional plane and that, on this plane, there is space outside the circle and, hence, a boundary. But that containing space is unnecessary. The mathematical abstraction exists with or without the containing space. It is perfectly well expressed as above -- the range of coordinates from 0 up to but not including 360 degrees along with a rule that the "0" end is adjacent to the "almost 360" end. That is an example of a finite one dimensional "manifold".

A gentle introduction to this sort of thing is "Sphereland". https://www.amazon.com/dp/0064635740/?tag=pfamazon01-20

 

[DaveC426913]

Consider as a simple example, a circle. It has one dimension. The points on the circle can be given coordinates from 0 degrees up to but not including 360 degrees. There is no edge. Instead, the circle wraps around on itself.

To riff on jbriggs' example:

By extension it applies to the 3-dimensional universe. The universe can be wrapped around upon itself so that, if you travel in one direction long enough, you will (in theory) arrive back at your destination.

The naive image of this assumes that the curvature occurs in a higher 4th dimension, but that is not true - it does not require such a 4th dimension to do so.

 

[Hugh de Launay]

The mathematical abstraction exists without the containing space.

Thanks a lot for your explanation. Is such an abstraction applied to the "edge" (if any) of our universe?

 

[Hugh de Launay]

By extension it applies to the 3-dimensional universe. The universe can be wrapped around upon itself so that, if you travel in one direction long enough, you will (in theory) arrive back at your destination.

This is true if the observer begins and ends his/her trip inside our universe. Beyond being philosophical, what would an observer outside our universe observe about our universe? -- assuming some sense can be made of such a question.

 

[jbriggs444]

This is true if the observer begins and ends his/her trip inside our universe. Beyond being philosophical, what would an observer outside our universe observe about our universe? -- assuming some sense can be made of such a question.

It is philosophical. There need be no outside. Any speculation about an outside is just that.

 

[phinds]

It is philosophical. There need be no outside. Any speculation about an outside is just that.

I disagree that it is philosophical. I think it is nonsensical. "Universe" is, by definition, all there is. It is one thing to say that there might be a part of the universe that has different characteristics than the rest (and there is not at present any inkling that there is such a place) but even if there were, it would STILL be part of the universe, not "outside" it.

 

[jbriggs444]

Is such an abstraction applied to the "edge" (if any) of our universe?

Since no edge is required and no evidence for an edge is found, no edge is assumed. Instead, we use Occam's razor and take the simple background assumption that, on the largest scales, the universe is the same everywhere. https://en.wikipedia.org/wiki/Cosmological_principle. A universe with an edge would violate this principle. A universe that is finite but which wraps around on itself would not.

The abstract ideas of a finite but unbounded space or of an infinite and unbounded space give us confidence that we are not building our cosmological models on a self-contradictory foundation. Both possibilities are consistent with the evidence so far. There is no need to choose.

 

[berkeman]

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